Answer to Question #183967 in Statistics and Probability for Benita

Question

Apart from being in the education sector, Richfield also has a fleet of cars available for rent. 

Statistics shows that the Mercedes AMG G63 is the most rented car among their fleet and one in four customers request this make. If 5 of today’s rentals are selected, what is the probability that 2 clients would have rented an AMG G63?

Answer 1

$n = 5 \\ p = \frac{1}{4} = 0.25 \\ q = 1-p = 0.75 \\ P(X=2) = C^5_2(0.25)^2(0.75)^{5-2} \\ = \frac{5!}{2!(5-2)!} \times 0.25^2 \times 0.75^3 \\ = 10 \times 0.0625 \times 0.4218 \\ = 0.2636$